Question: Simplify the following expression: $r = \dfrac{9}{10x} - \dfrac{1}{2x}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10x$ and $2x$ $\lcm(10x, 2x) = 10x$ $ r = \dfrac{1}{1} \cdot \dfrac{9}{10x} - \dfrac{5}{5} \cdot \dfrac{1}{2x} $ $r = \dfrac{9}{10x} - \dfrac{5}{10x}$ $r = \dfrac{9 -5}{10x}$ $r = \dfrac{4}{10x}$ Simplify the expression by dividing the numerator and denominator by 2: $r = \dfrac{2}{5x}$